1. Field of the Invention
The present invention relates to a shape-measuring method for accurately measuring a surface shape of an optical element or a die for manufacturing the optical element, the surface shape being formed based on a design shape having multiple periodical design-level differences.
2. Description of the Related Art
With the improvement of performance in various optical devices such as an image pickup camera, a laser beam printer, a copying machine, and a semiconductor exposure apparatus, requirements for optical elements incorporated in those optical devices have become severer. In recent years, in particular, diffraction-grating optical elements utilizing a diffraction-grating phenomenon are used for various products. Many such diffraction-grating optical elements have a regular unevenness of several nanometers to several tens of micrometers on the surface to generate a phase difference of light, so that a diffraction phenomenon is generated. In order to accurately measure a surface shape of an optical element or a surface shape of a die for molding an optical element in this way, it is necessary to perform accurate fitting between measured data of multiple measuring points and the design shape so as to eliminate a setting error of a work. Here, the fitting between the measured data and the design shape includes not only matching of the measured data and the design shape but also moving a parameter of the design shape to fit the design shape with the measured data and performing predetermined conversions on the design shape and the measured data for fitting.
By the way, it is difficult to fit between the measured data of a surface to be measured which is formed based on a design shape having multiple periodical design-level differences and the design shape, because there is a level-difference portion. Therefore, as a method of fitting the measured data with the design shape, the following method is known. Specifically, an array of multiple measuring points at which the surface to be measured is measured is converted to an approximate shape such as an aspherical surface or a spherical surface without level differences by using the least square method, and the design shape used is a no-level-difference shape without a design-level difference. Then, the approximate shape and the no-level-difference shape are fitted (see Japanese Patent Application Laid-Open No. H11-167013). In the case of this structure, because there is no component of a level-difference portion, it is considered that the fitting itself can be performed easily.
However, in the case of the invention described in Japanese Patent Application Laid-Open No. H11-167013, the design shape for fitting with the approximate shape determined from the measured point sequence does not contain a level-difference-shape component, and hence fitting accuracy cannot be improved due to the influence of the level-difference-shape component contained in the approximate shape. In other words, the surface to be measured is a combination shape of a level-difference-shape component and a no-level-difference-shape component (for example, a curved-surface-shape component), and a shape-measuring machine measures along the combination shape. Therefore, the measured point sequence contains a no-level-difference-shape component and a level-difference-shape component. Therefore, the approximate shape determined by the least square method or the like also contains a level-difference-shape component. On the other hand, only a no-level-difference-shape component is used in the design shape for fitting.
Therefore, because the design shape does not contain a level-difference-shape component, the level-difference-shape component of the approximate shape is affected by measurement noise or the like when the fitting is performed, and hence the fitting accuracy cannot be improved. In other words, because the fitting is performed between the shape containing a level-difference-shape component and a shape containing a no-level-difference-shape component, it is difficult to perform the fitting accurately. If the fitting accuracy is not good, a work-setting error cannot be accurately eliminated. As a result, measuring accuracy is also decreased.